It seems Einstein's equivalence principle is neglecting time dilation. If an observer is at rest in an inertial reference frame, free of any gravitation, she will experience time flow at the "native" rate of a universe empty of mass and energy. However, an observer in free fall at the surface of the earth will experience time flow at a rate determined by earth's gravitation, which is slower than the native time flow rate. This seems to imply non-equivalence?
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4$\begingroup$ To an observer, their own flow of time is still the same to them. $\endgroup$– Jbag1212Commented Apr 21, 2021 at 18:08
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4$\begingroup$ The equivalence principle is a local equivalence, so you can't refer to anything else than the time you experience and the distance you measure. $\endgroup$– Jeanbaptiste RouxCommented Apr 21, 2021 at 18:14
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1$\begingroup$ This is not the statement of time dilation at all! $\endgroup$– PraharCommented Apr 21, 2021 at 18:29
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2$\begingroup$ Does this answer your question? Time dilation in a gravitational field and the equivalence principle $\endgroup$– jng224Commented Apr 21, 2021 at 18:36
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$\begingroup$ When I say time is a mystery to me, I will point out that throughout the Answers and Comments here as well as the linked Question, Answers and Comments, time is described as a reading on a clock in the respective reference frame. I believe that to be a significant aspect, but that does not explain what causes time flow. $\endgroup$– FritzSCommented Apr 21, 2021 at 19:38
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2 Answers
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Not only is the equivalence principle not ignoring time dilation, you can actually use the equivalence principle to derive gravitational time dilation.
The issue that you are running into is probably the most common issue in applying the equivalence principle. That is that the equivalence principle is strictly local. It cannot be applied over a region of spacetime which is large enough for tidal effects (spacetime curvature) to be noticed. The comparison of the free faller with some distant clock is a non-local comparison and the equivalence principle makes no claim about the outcome.
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$\begingroup$ I suspected time dilation could be derived from EEP! I was taught time dilation based on speed of light being constant as observed from all inertial reference frames, but I also knew that this was not the basis for Einstein's original derivation. Thanks $\endgroup$– FritzSCommented Apr 21, 2021 at 19:18
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There is no way for the observer knows about time dilation. The clock in the frame shows the local time, and there is no comparison with another clocks in distant places. Otherwise it is not a local frame.
answered Apr 21, 2021 at 18:26